1. Pour the milk and coconut milk into a food processor and process gently until combined. Add half of the ice cream and process gently, then add the remaining ice cream and process until smooth.
2. Add the bananas and process well, then add the pineapple chunks and papya and process until smooth.
3. Pour the mixture into tall glasses, sprinkle over the grated coconut, and decorate the rims with wedges of fresh pineapple. Serve at once.